Deconfinement and universality in the 3D U(1) lattice gauge theory at finite temperature: study in the dual formulation

TL;DR

This paper investigates the critical behavior of the 3D U(1) lattice gauge theory at finite temperature using dual formulation, analytical RG equations, and numerical simulations to verify universality and locate the phase transition.

Contribution

It provides a combined analytical and numerical study of the deconfinement transition in 3D U(1) lattice gauge theory, including RG analysis and critical index calculations.

Findings

Validated the Svetitsky-Yaffe conjecture for the model

Located the critical points for various temporal extents

Computed critical indices and correlation lengths

Abstract

We study analytically and numerically the three-dimensional U(1) lattice gauge theory at finite temperature in the dual formulation. For an appropriate disorder operator, we obtain the renormalization group equations describing the critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky-Yaffe conjecture regarding the critical behavior of the lattice U(1) model. Furthermore, we perform numerical simulations of the model for $N_t = 1, 2, 4, 8$ and compute, by a cluster algorithm, the dual correlation functions and the corresponding second moment correlation length. In this way we locate the position of the critical point and calculate critical indices.